# No SInE strategy applied
# Trying AutoSched0 for 161 seconds
# AutoSched0-Mode selected heuristic G_E___302_C18_F1_URBAN_RG_S04BN
# and selection function PSelectComplexExceptUniqMaxHorn.
#
# Preprocessing time       : 0.020 s

# Proof found!
# SZS status Theorem
# SZS output start CNFRefutation
fof(t27_field_16, axiom, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~(v8_ordinal1(X2)))=>![X3]:((((((((((((~(v2_struct_0(X3))&~(v6_struct_0(X3)))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>k3_ring_3(X3)=X1)))), file('field_16/field_16__t46_field_16', t27_field_16)).
fof(t46_field_16, conjecture, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~(v8_ordinal1(X2)))=>![X3]:((((((((((((~(v2_struct_0(X3))&~(v6_struct_0(X3)))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>(r1_struct_0(k8_ring_3(X3),X4)<=>k2_binom(X3,X4,X1)=X4)))))), file('field_16/field_16__t46_field_16', t46_field_16)).
fof(dt_k5_field_16, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k5_field_16(X1))&v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), file('field_16/field_16__t46_field_16', dt_k5_field_16)).
fof(l65_field_16, axiom, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~(v8_ordinal1(X2)))=>![X3]:((((((((((((~(v2_struct_0(X3))&~(v6_struct_0(X3)))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>(k3_funct_2(u1_struct_0(X3),u1_struct_0(X3),k5_field_16(X3),X4)=X4<=>r1_struct_0(k8_ring_3(X3),X4))))))), file('field_16/field_16__t46_field_16', l65_field_16)).
fof(d6_field_16, axiom, ![X1]:(((((((((~(v2_struct_0(X1))&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:(((v1_funct_1(X2)&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))=>(X2=k5_field_16(X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X2,X3)=k2_binom(X1,X3,k3_ring_3(X1)))))), file('field_16/field_16__t46_field_16', d6_field_16)).
fof(c_0_5, plain, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~v8_ordinal1(X2))=>![X3]:((((((((((((~v2_struct_0(X3)&~v6_struct_0(X3))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>k3_ring_3(X3)=X1)))), inference(fof_simplification,[status(thm)],[t27_field_16])).
fof(c_0_6, negated_conjecture, ~(![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~v8_ordinal1(X2))=>![X3]:((((((((((((~v2_struct_0(X3)&~v6_struct_0(X3))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>(r1_struct_0(k8_ring_3(X3),X4)<=>k2_binom(X3,X4,X1)=X4))))))), inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t46_field_16])])).
fof(c_0_7, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>((v1_funct_1(k5_field_16(X1))&v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))), inference(fof_simplification,[status(thm)],[dt_k5_field_16])).
fof(c_0_8, plain, ![X33, X34, X35]:(~v7_ordinal1(X33)|~v1_int_2(X33)|(~v7_ordinal1(X34)|v8_ordinal1(X34)|(v2_struct_0(X35)|v6_struct_0(X35)|~v13_algstr_0(X35)|~v33_algstr_0(X35)|~v2_rlvect_1(X35)|~v3_rlvect_1(X35)|~v4_rlvect_1(X35)|~v4_vectsp_1(X35)|~v5_vectsp_1(X35)|~v3_group_1(X35)|~v5_group_1(X35)|~l6_algstr_0(X35)|(k7_struct_0(X35)!=k1_newton(X33,X34)|k3_ring_3(X35)=X33)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])).
fof(c_0_9, negated_conjecture, ((v7_ordinal1(esk1_0)&v1_int_2(esk1_0))&((v7_ordinal1(esk2_0)&~v8_ordinal1(esk2_0))&((((((((((((~v2_struct_0(esk3_0)&~v6_struct_0(esk3_0))&v13_algstr_0(esk3_0))&v33_algstr_0(esk3_0))&v2_rlvect_1(esk3_0))&v3_rlvect_1(esk3_0))&v4_rlvect_1(esk3_0))&v4_vectsp_1(esk3_0))&v5_vectsp_1(esk3_0))&v3_group_1(esk3_0))&v5_group_1(esk3_0))&l6_algstr_0(esk3_0))&(k7_struct_0(esk3_0)=k1_newton(esk1_0,esk2_0)&(m1_subset_1(esk4_0,u1_struct_0(esk3_0))&((~r1_struct_0(k8_ring_3(esk3_0),esk4_0)|k2_binom(esk3_0,esk4_0,esk1_0)!=esk4_0)&(r1_struct_0(k8_ring_3(esk3_0),esk4_0)|k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])).
fof(c_0_10, plain, ![X1]:((v7_ordinal1(X1)&v1_int_2(X1))=>![X2]:((v7_ordinal1(X2)&~v8_ordinal1(X2))=>![X3]:((((((((((((~v2_struct_0(X3)&~v6_struct_0(X3))&v13_algstr_0(X3))&v33_algstr_0(X3))&v2_rlvect_1(X3))&v3_rlvect_1(X3))&v4_rlvect_1(X3))&v4_vectsp_1(X3))&v5_vectsp_1(X3))&v3_group_1(X3))&v5_group_1(X3))&l6_algstr_0(X3))=>(k7_struct_0(X3)=k1_newton(X1,X2)=>![X4]:(m1_subset_1(X4,u1_struct_0(X3))=>(k3_funct_2(u1_struct_0(X3),u1_struct_0(X3),k5_field_16(X3),X4)=X4<=>r1_struct_0(k8_ring_3(X3),X4))))))), inference(fof_simplification,[status(thm)],[l65_field_16])).
fof(c_0_11, plain, ![X1]:(((((((((~v2_struct_0(X1)&v13_algstr_0(X1))&v2_rlvect_1(X1))&v3_rlvect_1(X1))&v4_rlvect_1(X1))&v4_vectsp_1(X1))&v5_vectsp_1(X1))&v3_group_1(X1))&l6_algstr_0(X1))=>![X2]:(((v1_funct_1(X2)&v1_funct_2(X2,u1_struct_0(X1),u1_struct_0(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))))=>(X2=k5_field_16(X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X2,X3)=k2_binom(X1,X3,k3_ring_3(X1)))))), inference(fof_simplification,[status(thm)],[d6_field_16])).
fof(c_0_12, plain, ![X28]:(((v1_funct_1(k5_field_16(X28))|(v2_struct_0(X28)|~v13_algstr_0(X28)|~v2_rlvect_1(X28)|~v3_rlvect_1(X28)|~v4_rlvect_1(X28)|~v4_vectsp_1(X28)|~v5_vectsp_1(X28)|~v3_group_1(X28)|~l6_algstr_0(X28)))&(v1_funct_2(k5_field_16(X28),u1_struct_0(X28),u1_struct_0(X28))|(v2_struct_0(X28)|~v13_algstr_0(X28)|~v2_rlvect_1(X28)|~v3_rlvect_1(X28)|~v4_rlvect_1(X28)|~v4_vectsp_1(X28)|~v5_vectsp_1(X28)|~v3_group_1(X28)|~l6_algstr_0(X28))))&(m1_subset_1(k5_field_16(X28),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X28),u1_struct_0(X28))))|(v2_struct_0(X28)|~v13_algstr_0(X28)|~v2_rlvect_1(X28)|~v3_rlvect_1(X28)|~v4_rlvect_1(X28)|~v4_vectsp_1(X28)|~v5_vectsp_1(X28)|~v3_group_1(X28)|~l6_algstr_0(X28)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])).
cnf(c_0_13, plain, (v8_ordinal1(X2)|v2_struct_0(X3)|v6_struct_0(X3)|k3_ring_3(X3)=X1|~v7_ordinal1(X1)|~v1_int_2(X1)|~v7_ordinal1(X2)|~v13_algstr_0(X3)|~v33_algstr_0(X3)|~v2_rlvect_1(X3)|~v3_rlvect_1(X3)|~v4_rlvect_1(X3)|~v4_vectsp_1(X3)|~v5_vectsp_1(X3)|~v3_group_1(X3)|~v5_group_1(X3)|~l6_algstr_0(X3)|k7_struct_0(X3)!=k1_newton(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8])).
cnf(c_0_14, negated_conjecture, (k7_struct_0(esk3_0)=k1_newton(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_15, negated_conjecture, (v1_int_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_16, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_17, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_18, negated_conjecture, (~v8_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
fof(c_0_19, plain, ![X29, X30, X31, X32]:((k3_funct_2(u1_struct_0(X31),u1_struct_0(X31),k5_field_16(X31),X32)!=X32|r1_struct_0(k8_ring_3(X31),X32)|~m1_subset_1(X32,u1_struct_0(X31))|k7_struct_0(X31)!=k1_newton(X29,X30)|(v2_struct_0(X31)|v6_struct_0(X31)|~v13_algstr_0(X31)|~v33_algstr_0(X31)|~v2_rlvect_1(X31)|~v3_rlvect_1(X31)|~v4_rlvect_1(X31)|~v4_vectsp_1(X31)|~v5_vectsp_1(X31)|~v3_group_1(X31)|~v5_group_1(X31)|~l6_algstr_0(X31))|(~v7_ordinal1(X30)|v8_ordinal1(X30))|(~v7_ordinal1(X29)|~v1_int_2(X29)))&(~r1_struct_0(k8_ring_3(X31),X32)|k3_funct_2(u1_struct_0(X31),u1_struct_0(X31),k5_field_16(X31),X32)=X32|~m1_subset_1(X32,u1_struct_0(X31))|k7_struct_0(X31)!=k1_newton(X29,X30)|(v2_struct_0(X31)|v6_struct_0(X31)|~v13_algstr_0(X31)|~v33_algstr_0(X31)|~v2_rlvect_1(X31)|~v3_rlvect_1(X31)|~v4_rlvect_1(X31)|~v4_vectsp_1(X31)|~v5_vectsp_1(X31)|~v3_group_1(X31)|~v5_group_1(X31)|~l6_algstr_0(X31))|(~v7_ordinal1(X30)|v8_ordinal1(X30))|(~v7_ordinal1(X29)|~v1_int_2(X29)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])).
fof(c_0_20, plain, ![X24, X25, X26]:((X25!=k5_field_16(X24)|(~m1_subset_1(X26,u1_struct_0(X24))|k3_funct_2(u1_struct_0(X24),u1_struct_0(X24),X25,X26)=k2_binom(X24,X26,k3_ring_3(X24)))|(~v1_funct_1(X25)|~v1_funct_2(X25,u1_struct_0(X24),u1_struct_0(X24))|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X24),u1_struct_0(X24)))))|(v2_struct_0(X24)|~v13_algstr_0(X24)|~v2_rlvect_1(X24)|~v3_rlvect_1(X24)|~v4_rlvect_1(X24)|~v4_vectsp_1(X24)|~v5_vectsp_1(X24)|~v3_group_1(X24)|~l6_algstr_0(X24)))&((m1_subset_1(esk5_2(X24,X25),u1_struct_0(X24))|X25=k5_field_16(X24)|(~v1_funct_1(X25)|~v1_funct_2(X25,u1_struct_0(X24),u1_struct_0(X24))|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X24),u1_struct_0(X24)))))|(v2_struct_0(X24)|~v13_algstr_0(X24)|~v2_rlvect_1(X24)|~v3_rlvect_1(X24)|~v4_rlvect_1(X24)|~v4_vectsp_1(X24)|~v5_vectsp_1(X24)|~v3_group_1(X24)|~l6_algstr_0(X24)))&(k3_funct_2(u1_struct_0(X24),u1_struct_0(X24),X25,esk5_2(X24,X25))!=k2_binom(X24,esk5_2(X24,X25),k3_ring_3(X24))|X25=k5_field_16(X24)|(~v1_funct_1(X25)|~v1_funct_2(X25,u1_struct_0(X24),u1_struct_0(X24))|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X24),u1_struct_0(X24)))))|(v2_struct_0(X24)|~v13_algstr_0(X24)|~v2_rlvect_1(X24)|~v3_rlvect_1(X24)|~v4_rlvect_1(X24)|~v4_vectsp_1(X24)|~v5_vectsp_1(X24)|~v3_group_1(X24)|~l6_algstr_0(X24))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])).
cnf(c_0_21, plain, (m1_subset_1(k5_field_16(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_22, negated_conjecture, (l6_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_23, negated_conjecture, (v3_group_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_24, negated_conjecture, (v5_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_25, negated_conjecture, (v4_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_26, negated_conjecture, (v4_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_27, negated_conjecture, (v3_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_28, negated_conjecture, (v2_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_29, negated_conjecture, (v13_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_30, negated_conjecture, (~v2_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_31, plain, (v1_funct_2(k5_field_16(X1),u1_struct_0(X1),u1_struct_0(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_32, plain, (v1_funct_1(k5_field_16(X1))|v2_struct_0(X1)|~v13_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
cnf(c_0_33, negated_conjecture, (k3_ring_3(X1)=esk1_0|v6_struct_0(X1)|v2_struct_0(X1)|k7_struct_0(X1)!=k7_struct_0(esk3_0)|~l6_algstr_0(X1)|~v5_group_1(X1)|~v3_group_1(X1)|~v5_vectsp_1(X1)|~v4_vectsp_1(X1)|~v4_rlvect_1(X1)|~v3_rlvect_1(X1)|~v2_rlvect_1(X1)|~v33_algstr_0(X1)|~v13_algstr_0(X1)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14]), c_0_15]), c_0_16]), c_0_17])]), c_0_18])).
cnf(c_0_34, negated_conjecture, (v5_group_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_35, negated_conjecture, (v33_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_36, negated_conjecture, (~v6_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_37, plain, (k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),k5_field_16(X1),X2)=X2|v2_struct_0(X1)|v6_struct_0(X1)|v8_ordinal1(X4)|~r1_struct_0(k8_ring_3(X1),X2)|~m1_subset_1(X2,u1_struct_0(X1))|k7_struct_0(X1)!=k1_newton(X3,X4)|~v13_algstr_0(X1)|~v33_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v7_ordinal1(X4)|~v7_ordinal1(X3)|~v1_int_2(X3)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_38, negated_conjecture, (r1_struct_0(k8_ring_3(esk3_0),esk4_0)|k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_39, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_40, plain, (k3_funct_2(u1_struct_0(X2),u1_struct_0(X2),X1,X3)=k2_binom(X2,X3,k3_ring_3(X2))|v2_struct_0(X2)|X1!=k5_field_16(X2)|~m1_subset_1(X3,u1_struct_0(X2))|~v1_funct_1(X1)|~v1_funct_2(X1,u1_struct_0(X2),u1_struct_0(X2))|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2))))|~v13_algstr_0(X2)|~v2_rlvect_1(X2)|~v3_rlvect_1(X2)|~v4_rlvect_1(X2)|~v4_vectsp_1(X2)|~v5_vectsp_1(X2)|~v3_group_1(X2)|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])).
cnf(c_0_41, negated_conjecture, (m1_subset_1(k5_field_16(esk3_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk3_0),u1_struct_0(esk3_0))))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29])]), c_0_30])).
cnf(c_0_42, negated_conjecture, (v1_funct_2(k5_field_16(esk3_0),u1_struct_0(esk3_0),u1_struct_0(esk3_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29])]), c_0_30])).
cnf(c_0_43, negated_conjecture, (v1_funct_1(k5_field_16(esk3_0))), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29])]), c_0_30])).
cnf(c_0_44, negated_conjecture, (k3_ring_3(esk3_0)=esk1_0), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_33]), c_0_22]), c_0_34]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_35]), c_0_29])]), c_0_36]), c_0_30])).
cnf(c_0_45, negated_conjecture, (k3_funct_2(u1_struct_0(esk3_0),u1_struct_0(esk3_0),k5_field_16(esk3_0),esk4_0)=esk4_0|k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0|v8_ordinal1(X1)|k1_newton(X2,X1)!=k7_struct_0(esk3_0)|~v1_int_2(X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_39]), c_0_22]), c_0_34]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_35]), c_0_29])]), c_0_36]), c_0_30])).
cnf(c_0_46, negated_conjecture, (k3_funct_2(u1_struct_0(esk3_0),u1_struct_0(esk3_0),k5_field_16(esk3_0),X1)=k2_binom(esk3_0,X1,esk1_0)|~m1_subset_1(X1,u1_struct_0(esk3_0))), inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_43]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29])]), c_0_30]), c_0_44])).
cnf(c_0_47, negated_conjecture, (k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0|v8_ordinal1(X1)|k1_newton(X2,X1)!=k7_struct_0(esk3_0)|~v1_int_2(X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_39])])).
cnf(c_0_48, negated_conjecture, (k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0|v8_ordinal1(X1)|k1_newton(esk1_0,X1)!=k7_struct_0(esk3_0)|~v7_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_15]), c_0_17])])).
cnf(c_0_49, plain, (r1_struct_0(k8_ring_3(X1),X2)|v2_struct_0(X1)|v6_struct_0(X1)|v8_ordinal1(X4)|k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),k5_field_16(X1),X2)!=X2|~m1_subset_1(X2,u1_struct_0(X1))|k7_struct_0(X1)!=k1_newton(X3,X4)|~v13_algstr_0(X1)|~v33_algstr_0(X1)|~v2_rlvect_1(X1)|~v3_rlvect_1(X1)|~v4_rlvect_1(X1)|~v4_vectsp_1(X1)|~v5_vectsp_1(X1)|~v3_group_1(X1)|~v5_group_1(X1)|~l6_algstr_0(X1)|~v7_ordinal1(X4)|~v7_ordinal1(X3)|~v1_int_2(X3)), inference(split_conjunct,[status(thm)],[c_0_19])).
cnf(c_0_50, negated_conjecture, (~r1_struct_0(k8_ring_3(esk3_0),esk4_0)|k2_binom(esk3_0,esk4_0,esk1_0)!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_9])).
cnf(c_0_51, negated_conjecture, (k2_binom(esk3_0,esk4_0,esk1_0)=esk4_0), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_14]), c_0_16])]), c_0_18])).
cnf(c_0_52, negated_conjecture, (r1_struct_0(k8_ring_3(esk3_0),X1)|v8_ordinal1(X2)|k2_binom(esk3_0,X1,esk1_0)!=X1|k1_newton(X3,X2)!=k7_struct_0(esk3_0)|~m1_subset_1(X1,u1_struct_0(esk3_0))|~v1_int_2(X3)|~v7_ordinal1(X2)|~v7_ordinal1(X3)), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_46]), c_0_22]), c_0_34]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_35]), c_0_29])]), c_0_36]), c_0_30])).
cnf(c_0_53, negated_conjecture, (~r1_struct_0(k8_ring_3(esk3_0),esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
cnf(c_0_54, negated_conjecture, (v8_ordinal1(X1)|k1_newton(X2,X1)!=k7_struct_0(esk3_0)|~v1_int_2(X2)|~v7_ordinal1(X1)|~v7_ordinal1(X2)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_51]), c_0_39])]), c_0_53])).
cnf(c_0_55, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_14]), c_0_15]), c_0_16]), c_0_17])]), c_0_18]), ['proof']).
# SZS output end CNFRefutation
# Proof object total steps             : 56
# Proof object clause steps            : 41
# Proof object formula steps           : 15
# Proof object conjectures             : 37
# Proof object clause conjectures      : 34
# Proof object formula conjectures     : 3
# Proof object initial clauses used    : 27
# Proof object initial formulas used   : 5
# Proof object generating inferences   : 13
# Proof object simplifying inferences  : 102
# Training examples: 0 positive, 0 negative
# Parsed axioms                        : 5
# Removed by relevancy pruning/SinE    : 0
# Initial clauses                      : 29
# Removed in clause preprocessing      : 0
# Initial clauses in saturation        : 29
# Processed clauses                    : 44
# ...of these trivial                  : 0
# ...subsumed                          : 0
# ...remaining for further processing  : 44
# Other redundant clauses eliminated   : 0
# Clauses deleted for lack of memory   : 0
# Backward-subsumed                    : 6
# Backward-rewritten                   : 2
# Generated clauses                    : 18
# ...of the previous two non-trivial   : 17
# Contextual simplify-reflections      : 0
# Paramodulations                      : 17
# Factorizations                       : 0
# NegExts                              : 0
# Equation resolutions                 : 1
# Propositional unsat checks           : 0
#    Propositional check models        : 0
#    Propositional check unsatisfiable : 0
#    Propositional clauses             : 0
#    Propositional clauses after purity: 0
#    Propositional unsat core size     : 0
#    Propositional preprocessing time  : 0.000
#    Propositional encoding time       : 0.000
#    Propositional solver time         : 0.000
#    Success case prop preproc time    : 0.000
#    Success case prop encoding time   : 0.000
#    Success case prop solver time     : 0.000
# Current number of processed clauses  : 36
#    Positive orientable unit clauses  : 20
#    Positive unorientable unit clauses: 0
#    Negative unit clauses             : 4
#    Non-unit-clauses                  : 12
# Current number of unprocessed clauses: 1
# ...number of literals in the above   : 6
# Current number of archived formulas  : 0
# Current number of archived clauses   : 8
# Clause-clause subsumption calls (NU) : 167
# Rec. Clause-clause subsumption calls : 4
# Non-unit clause-clause subsumptions  : 4
# Unit Clause-clause subsumption calls : 9
# Rewrite failures with RHS unbound    : 0
# BW rewrite match attempts            : 1
# BW rewrite match successes           : 1
# Condensation attempts                : 0
# Condensation successes               : 0
# Termbank termtop insertions          : 4952

# -------------------------------------------------
# User time                : 0.025 s
# System time              : 0.000 s
# Total time               : 0.025 s
# Maximum resident set size: 3532 pages
